Question

If sum of squares zeroes of polynomial f(x)=x2-8x+k is 40.Find k​​

Answer 1

Answer:

let zeroes of this polynomial are a and b

so a+b=8

ab=k

given : a^2 +b^2 =40

answer is 24

Step-by-step explanation:

applying formula

(a+b)^2 =a^2 +b^2 +ab

(8)^2=40+k

64=40+k

64-40=k

k=24

Answer 2

Answer:

Value of k is 24.

Step-by-step explanation:

Given :

Sum of squares of zeroes of the polynomial f(x) = x² - 8x + k is 40

Let α, β be the zeroes the given polynomial

So, Sum of squares of zeroes = α² + β² = 40

Comparing the given polynomial with ax² + bx + c we get

• a = 1
• b = - 8
• c = k

Sum of zeroes = α + β = - b/a = - ( - 8 ) / 1 = 8

Product of zeroes = αβ = c/a = k/1 = k

We know that

( α + β )² = α² + β² + 2αβ

Substituting the known values

( 8 )² = 40 + k

64 = 40 + k

k = 64 - 40

k = 24

Therefore the value of k is 24.